How to draw curved symmetric lines within a shape
Curves can be a little different from editing meshes but with a little practice can be easy to work with. The array and mirror modifiers also work with curves to help you get the symmetry you are after.



Here I have one small curve with an array and a mirror. You can see the red handles on the real curve piece. To get some thickness to the curve you only need to turn up the bevel depth. You can also use another curve as a bevel object to get a unique shape extruded along the length of the curve.



If you have a bad join between the array pieces like this



you can enable merge in the array modifier and increase the merge distance if needed. You should also adjust the handles on the curve so that the start and end of the curve are pointing straight at each other for a clean merge.



And if you have a non-circular bevel shape you may want to twist the points using CtrlT. With a square bevel you can get the twisted look you get on iron gates.



You can easily convert the curve to a mesh object with AltC